Make kron(a,b) preserve Adjoint-ness (#35755)

* kron(adjoint vector)

* tests

* docstring for kron

* the implementation

* better idea

Co-authored-by: Michael Abbott <me@escbook>

Author: mcabbott

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -221,6 +221,7 @@ similar(A::AdjOrTrans, ::Type{T}, dims::Dims{N}) where {T,N} = similar(A.parent,
 # sundry basic definitions
 parent(A::AdjOrTrans) = A.parent
 vec(v::TransposeAbsVec) = parent(v)
+vec(v::AdjointAbsVec{<:Real}) = parent(v)
 
 ### concatenation
 # preserve Adjoint/Transpose wrapper around vectors

stdlib/LinearAlgebra/src/dense.jl

@@ -341,11 +341,12 @@ end
 
 Kronecker tensor product of two vectors or two matrices.
 
-For vectors v and w, the Kronecker product is related to the outer product by
-`kron(v,w) == vec(w*transpose(v))` or
-`w*transpose(v) == reshape(kron(v,w), (length(w), length(v)))`.
+For real vectors `v` and `w`, the Kronecker product is related to the outer product by
+`kron(v,w) == vec(w * transpose(v))` or
+`w * transpose(v) == reshape(kron(v,w), (length(w), length(v)))`.
 Note how the ordering of `v` and `w` differs on the left and right
 of these expressions (due to column-major storage).
+For complex vectors, the outer product `w * v'` also differs by conjugation of `v`.
 
 # Examples
 ```jldoctest
@@ -400,6 +401,9 @@ kron(a::AbstractVector, b::AbstractVector) = vec(kron(reshape(a ,length(a), 1),
 kron(a::AbstractMatrix, b::AbstractVector) = kron(a, reshape(b, length(b), 1))
 kron(a::AbstractVector, b::AbstractMatrix) = kron(reshape(a, length(a), 1), b)
 
+kron(a::AdjointAbsVec, b::AdjointAbsVec) = adjoint(kron(adjoint(a), adjoint(b)))
+kron(a::AdjOrTransAbsVec, b::AdjOrTransAbsVec) = transpose(kron(transpose(a), transpose(b)))
+
 # Matrix power
 (^)(A::AbstractMatrix, p::Integer) = p < 0 ? power_by_squaring(inv(A), -p) : power_by_squaring(A, p)
 function (^)(A::AbstractMatrix{T}, p::Integer) where T<:Integer

stdlib/LinearAlgebra/test/adjtrans.jl

@@ -271,7 +271,7 @@ end
 
 @testset "Adjoint and Transpose vector vec methods" begin
     intvec = [1, 2]
-    @test vec(Adjoint(intvec)) == intvec
+    @test vec(Adjoint(intvec)) === intvec
     @test vec(Transpose(intvec)) === intvec
     cvec = [1 + 1im]
     @test vec(cvec')[1] == cvec[1]'

stdlib/LinearAlgebra/test/dense.jl

@@ -395,6 +395,17 @@ end
     @test kron(b',2) == [8 10 12]
 end
 
+@testset "kron adjoint" begin
+    a = [1+im, 2, 3]
+    b = [4, 5, 6+7im]
+    @test kron(a', b') isa Adjoint
+    @test kron(a', b') == kron(a, b)'
+    @test kron(transpose(a), b') isa Transpose
+    @test kron(transpose(a), b') == kron(permutedims(a), collect(b'))
+    @test kron(transpose(a), transpose(b)) isa Transpose
+    @test kron(transpose(a), transpose(b)) == transpose(kron(a, b))
+end
+
 @testset "issue #4796" begin
     dim=2
     S=zeros(Complex,dim,dim)